What gravitational field is generated by a massive quantum system in a spatial superposition? Despite decades of intensive theoretical and experimental research, we still do not know the answer. On the experimental side, the difficulty lies in the fact that gravity is weak and requires large masses to be detectable. However, it becomes increasingly difficult to generate spatial quantum superpositions for increasingly large masses, in light of the stronger environmental effects on such systems. Clearly, a delicate balance between the need for strong gravitational effects and weak decoherence should be found. We show that such a trade off could be achieved in an optomechanics scenario that allows to determine whether the gravitational field generated by a quantum system in a spatial superposition is in a coherent superposition or not. We estimate the magnitude of the effect and show that it offers perspectives for observability.
We present a simple calculation leading to the quantum gravitationally-induced decoherence of a spatial superposition of a massive object in the linear coupling regime. The point of this calculation is to illustrate that the gravitationally-induced collapse could be of the same origin as any other collapse, i.e. due to the entanglement between the system (here a massive object) and its environment (in this case gravity, but it could well be the electromagnetic or any other field). We then point out that, in some cases, one has to be careful when concluding that matter-wave interference of larg…
In this paper, we are exploring the feasibility of observing non-classical features of gravity in a low-energy regime in a quantum optomechanical experiment. If gravity is to have an underlying quantum nature, it should hold the most fundamental quantum characteristics such as the superposition principle and entanglement. Despite the weakness of gravity, in principle there is a chance, to observe such a quantum signature of the gravity by exploiting the quantum optomechanical techniques, without direct observation of graviton. We are investigating a new dynamical scheme called, gravitational q…
When a massive quantum body is put into a spatial superposition, it is of interest to consider the quantum aspects of the gravitational field sourced by the body. We argue that in order to understand how the body may become entangled with other massive bodies via gravitational interactions, it must be thought of as being entangled with its own Newtonian-like gravitational field. Thus, a Newtonian-like gravitational field must be capable of carrying quantum information. Our analysis supports the view that table-top experiments testing entanglement of systems interacting via gravity do probe the…
Atomic clocks can measure the gravitational redshift predicted by general relativity with great accuracy and for height differences as little as 1 cm. All existing experiments, however, involve the comparison of two independent clocks at different locations rather than a single clock in a delocalized quantum superposition. Here we present an interferometry scheme employing group-II-type atoms, such as Sr or Yb, capable of measuring the gravitational time dilation in a coherent superposition of atomic wave packets at two different heights. In contrast to other recent proposals, there is no need…
Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-Université PSL, Collège de France（卡斯勒-布罗塞尔实验室，索邦大学，法国国家科学研究中心，巴黎高等师范学院-巴黎文理研究大学，法兰西学院）；University of Waterloo（滑铁卢大学）；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）
We extend our earlier work on probing a gravitational cat state (gravcat)---see, arXiv:1504.03103 ---to the quantum superposition of two gravcats in an exemplary model and in Bose-Einstein condensates (BEC). In addition to its basic theoretical values in gravitational quantum physics and macroscopic quantum phenomena this investigation can provide some theoretical support to experimental proposals for measuring gravity-induced entanglement and the quantum nature of perturbative gravity. In the first part we consider cat states generated by double-well potentials. Approximated as two-level syst…
We study the superposition of primordial massive particles and compute the associated decoherence time scale in the radiation dominated universe. We observe that for lighter primordial particles with masses up to $10^7\,\rm{kg}$, the corresponding decoherence time scale is significantly larger than the age of the observable universe, demonstrating that a primordial particle would persist in a pure quantum state, with its wavefunction spreading freely. For heavier particles, they can still be in a quantum state while their position uncertainties are limited by the wavelength of background photo…
Spontaneous wave function collapse from non-local gravitational self-energy
State University of Tetovo（泰托沃国立大学）；California State University, Fresno（加州州立大学弗雷斯诺分校）；Universidade de Lisboa（里斯本大学）；Instituto de Astrofísica e Ciências do Espaco（天文与空间科学研究所）
Roger Penrose and the author share the proposal that the spatial superposition $|x_1\rangle+|x_2\rangle$ of a massive object collapses into its localized components $|x_1\rangle$ or $|x_2\rangle$ with the characteristic time $\hbar/E_Δ$ where $E_Δ$ is the gravitational self-energy excess of the superposition versus the localized states. Underlying arguments of such radical departure from standard quantum mechanics and different derivations of the rate equation are briefly recapitulated and discussed.
We analyze the recent proposal of measuring a quantum gravity phenomenon in the lab by entangling two particles gravitationally. We give a generally covariant description of this phenomenon, where the relevant effect turns out to be a quantum superposition of proper times. We point out that measurement of this effect would count as evidence for quantum superposition of spacetime geometries. This interpretation addresses objections appeared in the literature. We observe that the effect sheds light on the Planck mass, and argue that it is very plausibly a real effect.
We study the notion of causal orders for the cases of (classical and quantum) circuits and spacetime events. We show that every circuit can be immersed into a classical spacetime, preserving the compatibility between the two causal structures. Using the process matrix formalism, we analyse the realisations of the quantum switch using 4 and 3 spacetime events in classical spacetimes with fixed causal orders, and the realisation of a gravitational switch with only 2 spacetime events that features superpositions of different gravitational field configurations and their respective causal orders. W…
Non-local mass superpositions and optical clock interferometry in atomic ensemble quantum networks
University of Innsbruck（因斯布鲁克大学）；Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences（奥地利科学院量子光学和量子信息研究所）；Leibniz Universität Hannover（汉诺威莱布尼茨大学）；JILA, NIST and Department of Physics, University of Colorado（科罗拉多大学JILA、美国国家标准与技术研究院及物理系）；Center for Theory of Quantum Matter, University of Colorado（科罗拉多大学量子物质理论中心）
Taking the principles of quantum mechanics as they stand and applying them to gravity, leads to the conclusion that one might be able to generate superpositions of spacetimes, at least formally. We analyze such a possibility from an analogue gravity perspective. We present an analogue toy model consisting of a Bose-Einstein condensate in a double-well potential and identify the states that could potentially be interpreted as superposition of effective spacetimes. These states are unstable and the source of instability from a microscopic point of view can be related to the absence of a well-def…
We analyse a gedankenexperiment previously considered by Mari et al. that involves quantum superpositions of charged and/or massive bodies ("particles") under the control of the observers, Alice and Bob. In the electromagnetic case, we show that the quantization of electromagnetic radiation (which causes decoherence of Alice's particle) and vacuum fluctuations of the electromagnetic field (which limits Bob's ability to localize his particle to better than a charge-radius) both are essential for avoiding apparent paradoxes with causality and complementarity. We then analyze the gravitational ve…
The creation of delocalized coherent superpositions of quantum systems experiencing different relativistic effects is an important milestone in future research at the interface of gravity and quantum mechanics. This could be achieved by generating a superposition of quantum clocks that follow paths with different gravitational time dilation and investigating the consequences on the interference signal when they are eventually recombined. Light-pulse atom interferometry with elements employed in optical atomic clocks is a promising candidate for that purpose, but suffers from major challenges i…
The Schrodinger-Newton equation has frequently been studied as a nonlinear modification of the Schrodinger equation incorporating gravitational self-interaction. However, there is no evidence yet as to whether nature actually behaves this way. This work investigates a possible way to experimentally test gravitational self-interaction. The effect of self-gravity on interference of massive particles is studied by numerically solving the Schrodinger-Newton equation for a particle passing through a double-slit. The results show that the presence of gravitational self-interaction has an effect on t…
We propose a thought experiment, based on a mechanism that is reminiscent of Cavendish's torsion balance, to investigate the possible quantum nature of the gravitational field generated by the quantum superposition state of a massive system. Our proposal makes use of the dynamics of a ultra-stable optically levitated nanomechanical rotor endowed with a spin to generate a quantum angular superposition that is then tested through standard Ramsey-like scheme. Gravity manifests itself as an effective decoherence mechanism, whose strength is different-and, as we show, appreciable-in the classical a…
Observable signatures of the quantum nature of gravity at low energies have recently emerged as a promising new research field. One prominent avenue is to test for gravitationally induced entanglement between two mesoscopic masses prepared in spatial superposition. Here we analyze such proposals and what one can infer from them about the quantum nature of gravity, as well as the electromagnetic analogues of such tests. We show that it is not possible to draw conclusions about mediators: even within relativistic physics, entanglement generation can equally be described in terms of mediators or …
We review the Montevideo Interpretation of quantum mechanics, which is based on the use of real clocks to describe physics, using the framework recently introduced by Hoehn, Smith and Lock to treat the problem of time in generally covariant systems. The use of the new formalism makes the whole construction more accessible to readers without familiarity with totally constrained systems. We find that as in the original formulation, a fundamental mechanism of decoherence emerges that allows to supplement ordinary environmental decoherence and avoid its criticisms. Recent results on quantum comple…
We show that if a massive body is put in a quantum superposition of spatially separated states, the mere presence of a black hole in the vicinity of the body will eventually destroy the coherence of the superposition. This occurs because, in effect, the gravitational field of the body radiates soft gravitons into the black hole, allowing the black hole to acquire "which path" information about the superposition. A similar effect occurs for quantum superpositions of electrically charged bodies. We provide estimates of the decoherence time for such quantum superpositions. We believe that the fac…
The recent discovery of gravitational waves by the LIGO-Virgo collaboration created renewed interest in the investigation of alternative gravitational detector designs, such as small scale resonant detectors. In this article, it is shown how proposed small scale detectors can be tested by generating dynamical gravitational fields with appropriate distributions of moving masses. A series of interesting experiments will be possible with this setup. In particular, small scale detectors can be tested very early in the development phase and tests can be used to progress quickly in their development…
A small quantum system is studied which is a superposition of states localized in different positions in a static gravitational field. The time evolution of the correlation between different positions is investigated, and it is seen that there are two time scales for such an evolution (decoherence). Both time scales are inversely proportional to the red shift difference between the two points. These time scales correspond to decoherences which are linear and quadratic, respectively, in time.
Within any anticipated unifying theory of quantum gravity, it should be meaningful to combine the fundamental notions of quantum superposition and spacetime to obtain so-called "spacetime superpositions": that is, quantum superpositions of different spacetimes not related by a global coordinate transformation. Here we consider the quantum-gravitational effects produced by superpositions of periodically identified Minkowski spacetime (i.e.\ Minkowski spacetime with a periodic boundary condition) with different characteristic lengths. By coupling relativistic quantum matter to fields on such a s…
